The Climate Machine: The Faint Young-Sun Paradox

The Sun's intensity has increased about 30% over the past 4 billion years. Given that we can estimate the effective temperature from
Te = [ Fs (1-albedo) / (4*sigma)]1/4
where sigma is the Stefan Boltzman constant and albedo is the percent of sunlight reflected by the Earth.
We derived this in the simple Earth energy balance model.

If we replace Fs by .7*Fs, we find that Te becomes 233 oK rather than 255 oK. If the emissivity of the atmosphere remains unchanged (0.75) the surface temperature is given by a basic greenhouse calculation at 262oK. Moreover, the greenhouse effect due to water vapor was probably considerably less than it is today as the cooler atmosphere presumably held considerably less moisture and therefore the emissivity would probably be less than 0.75.

How then could liquid water exist over much of Earth as suggested by geologic evidence?
One explanation is that a stronger greenhouse effect existed due to elevated levels of CO2 due to active levels of early volcanism which releases CO2 into the atmosphere. Over time, weathering and the oceans may have removed large portions of CO2 from the atmosphere and our present climate state may have evolved.